A shadow instrument

Why does a tree’s shadow move and change length?

Move the Sun and watch the shadow of a marked point 5 metres above level ground.

Before you try

If the Sun is lower in the sky, does this shadow become longer, shorter, or stay the same?

A model instrument beside a miniature tree. Ruler inlays are spaced 5 m apart. The reference stroke measures the marked reference point; the rim pointer indicates Sun direction. Compass in this fixed camera: N ↙ · E ↘ · S ↗ · W ↖.

Height above the horizon

Clockwise from north: N 0° · E 90° · S 180° · W 270°

Shadow length
5.00 m
Shadow bearing
315°

Follow the light to the ground

The shadow points away from the Sun. Lower sunlight meets the ground farther from the reference, making a longer shadow. Moving the Sun around the horizon changes the shadow’s direction. At a fixed elevation, that rotation does not change its length.

Geometry, assumptions, and sources

In the right triangle, tan(elevation) = height ÷ shadow length. Rearranging gives shadow length = height ÷ tan(elevation).

The reference is upright on level ground and sunlight is parallel. The tree model provides context; its canopy shadow is not calculated. This experiment omits canopy gaps, soft edges, slopes, weather, and atmospheric refraction. The independent controls do not reproduce a daily or seasonal solar path. The rim pointer shows horizontal Sun direction, not the Sun’s physical height or distance.

Try the idea somewhere new

If the reference height doubles while the Sun stays fixed, what happens to its shadow length?